This invention relates to a signal processing apparatus and method, a recording medium and a program, and more particularly to a signal processing apparatus and method, a recording medium and a program by which signal components of different musical intervals of an audio signal can be obtained.
Various musical interval estimation methods have been proposed wherein signal components obtained by sampling a digital audio (music) signal with a predetermined sampling frequency are classified into signal components of different musical intervals (scales) such as, for example, C, C#, D, D#, E, F, F#, G, G#, A, A# and B (which correspond to do, do#, re, re#, mi, fa, fa#, so, so#, la, la# and ti, respectively). Such estimation of musical intervals of an audio signal is utilized, for example, for automatic music transcription, music analysis (melody analysis) and so forth.
The twelve musical intervals of C, C#, D, D#, E, F, F#, G, G#, A, A# and B construct one octave, and the frequencies of musical intervals of one octave are equal to twice those of musical intervals lower by one octave than the musical intervals. In other words, musical intervals are distributed logarithmically (exponentially) with respect to the frequency. For example, if the frequency (center frequency) of the musical interval of A (la) of a certain octave is 440 Hz, then the frequency of the musical interval of A (la) higher by one octave is 880 Hz which is equal to twice 440 Hz. Meanwhile, for example, the difference in frequency (center frequency) between C4 (do) and C#4 (do#) which are adjacent each other is approximately 6 Hz in the octave 2 on the low frequency region side, but is approximately 123 Hz in the octave 6 on the high frequency region side.
Also the frequency bands (bandwidths) of the musical intervals of a certain octave are twice those of the musical intervals lower by one octave.
Incidentally, as an estimation method of musical intervals of an audio signal (signal components of musical intervals included in the audio signal), for example, a method which uses short-time Fourier transform and a method which uses wavelet conversion are available.
The short-time Fourier transform analyzes frequency components at frequencies spaced at equal distances from each other while musical intervals are distributed logarithmically with respect to the frequency as described above. Therefore, according to a musical interval estimation method which uses the short-time Fourier transform, there is a tendency that the frequency resolution is insufficient on the low frequency region side but is excessive on the high frequency region side.
In particular, in the short-time Fourier transform, not only high musical intervals, that is, musical intervals having broad frequency bands, but also low musical intervals, that is, musical intervals having narrow frequency band, are analyzed with frequencies spaced at equal distances from each other. Therefore, the frequency resolution of high musical intervals is relatively high while the frequency resolution of low musical intervals is relatively low.
On the other hand, if it is tried to assure a sufficient frequency resolution on the low frequency region side, then the time resolution becomes excessive on the low frequency region side. On the contrary, if it is tried to assure a sufficient and necessary frequency resolution on the high frequency region side, then the time resolution becomes insufficient on the high frequency region side.
Further, when the short-time Fourier transform is used to estimate musical intervals, it is necessary to take it consideration that musical intervals are distributed logarithmically with respect to the frequency to apply a non-linear process for a result of analysis of frequency components at equal distances obtained by the Fourier transform. Due to the non-linear process, the musical interval estimation method which uses the short-time Fourier transform has a problem that the process is complicated.
Thus, according to a musical interval estimation method which uses the wavelet conversion, it is considered that musical intervals can be estimated with an ideal time-base resolution and frequency resolution by using a basis function which can extract a 1/12 octave (one musical interval).
As a further musical interval estimation method for an audio signal, a method is available wherein a BPF (Band Pass Filter) bank which includes one BPF for each musical interval of each octave is used to obtain signal components of the musical intervals of the octaves as disclosed, for example, in Japanese Patent Publication No. Sho 61-26067. However, where a BPF bank is used, it is necessary to design the BPFs so that, for example, an appropriate time resolution and frequency resolution may be obtained for each octave.
However, where the method which uses the wavelet conversion or a BPF bank is applied, for example, to analysis of musical intervals for the overall audio frequencies, a very great amount of arithmetic operation is required, and therefore, the methods are poor in practical use.